Suppose S CR3 is the intersection of B(0; 2) and the cylinder {(1, y, z) :...
14. Let S be the cylinder {(x, y, z)| x2 +22 = 25,0 SY <2}. Orient S by the outward pointing normal n = (x/5,0,2/5). Evaluate Fds, where F(x, y, z) = (x – 2, y, x + 2). Hint: The area of a cylinder of radius r and height h is 2nrh.
(For 5b, please use the y-axis as the axis of symmetry for the cylinder) 5) a-b Set-up the flux integrals for the given surfaces in the variables indicated. Your final answer should be a scalar- valued double integral. That is, the double integral should does not contain any vector quantities. The differential is given. Do not solve the integrals you setup in a. and b. No work is needed for a-b. a. F(x, y, z) = 5î + 10ủ +...
evaluate JJ. (< –Y) A. ) Integrate f(x, y, z) = x2 + y2 + 22 over the cylinder x2 + y2 < 2,-2 <2<3 (IL dx dy dz Feraluate
use stokes theorem b. F(x, y, z) =<z?, y, z>, S: 2 = 19x2 - y2, and Cis the trace of S In the xy-plane (positively oriented). Sketch S and C, then Evaluate.
Let Yı, Y, have the joint density S 2, 0 < y2 <yi <1 f(y1, y2) = 0, elsewhere. Use the method of transformation to derive the joint density function for U1 = Y/Y2,U2 = Y2, and then derive the marginal density of U1.
S 6 Calculate the fleux SSF. ds, where I la, y, z)= <0? 2², 227 and S is the finite cylinder (with top and bottom) given by x² + y² = 1, 2 = 0, Z = 3,
F(x, y, z) =< P, Q, R >=<-y +z,x-z,x-y> S: z = 9 - x2 - y2 and z>0 (9a) Evaluate W= $ P dx + Qdy + Rdz с
PLEASE ANSWER NUMBER 5 4. (1 point) Evaluate the triple integral on the given domain slf (x² + y2 +22)3/2 dxdydz where G={(x,y,z): x² + y2 +z? <4} 5. (2 points) Evaluate the volume of the solid bounded by the paraboloids z=16– x2 - y2 and z = x² + y2
A flat plate has an area D specified by the constraints y> 0 and 1 < x2 + y2 <16. If the density is given by p(x, y) = y y (22 +32) then the mass of the plate is given by the double integral SJ p(,y) dedy D Evaluate the double integral using polar coordinates z=r cos (O) and y=r sin (O). SJ p(x,y) d.ody= D Preferably leave you answer in terms of fractions, exponentials or 7. If you...
Find the volume of the solid enclosed by the paraboloid z = 5x2 + 5y 2 and the planes x = 0, y = 3, y = x, z = 1225 3 Evaluate the double integral. SS 9. y2 - xdA, D = {lar,y) |0<y< 4,0 <r<y} 24 Evaluate the double integral. I, 4xy dA, D is the triangular region with vertices (0,0), (1, 2), and (0,